The present invention relates to an electron beam drawing method and, more particularly, to a matching correcting method suitable to directly draw an electron beam by a matching mark detecting method.
In the case of manufacturing semiconductor devices by directly drawing an electron beam, it is important to match patterns of respective layers.
An arrangement of a number of semiconductor device chips on a semiconductor wafer is previously accurately determined at the design stage. Therefore, in theory, it is sufficient to draw so as to overlap the coordinates of the relevant chip every layer. However, in the actual conditions, there exist deformation of the water and the like in association with the rotating, shifting, and processing steps to set the wafer into an electron beam drawing apparatus. As disclosed in JP-A-57-204127, upon drawing, it is necessary to input those information and to correct a deflecting system of an electron beam and then to draw.
Namely, to measure rotation amount, shift amount, and deformation amount of the wafer, the arrangement of the semiconductor device chips is divided into matching blocks, and the matching marks formed at four corners of each matching block are detected by the electron beam. The rotation, shift, and deformation amounts are calculated from the coordinates of the detected matching marks. The deflection correcting system of the electron beam is corrected, then the electron beam is drawn.
The correcting equations at this time are expressed by the equations (1). ##EQU1##
In the equations (1), X and Y denote coordinates from the center of a block, and .DELTA.X and .DELTA.Y indicate correction amounts, A, B, C, D, A', B', C', and D' are called correction coefficients and have the following meanings, respectively.
A : gain term in the X direction, PA1 B : rotational term regarding a Y axis, PA1 C : trapezoid term which is symmetrical with respect to the Y axis, PA1 D : shift term in the X direction, PA1 A': rotational term regarding an X axis, PA1 B': gain term in the Y direction, PA1 C': trapezoid term which is symmetrical with respect to the X axis, PA1 D': shift term in the Y direction.
The correction coefficients A to D' are calculated by the following procedure. Four matching marks are set in the first to fourth quadrants of a block, respectively. The coordinates of the four matching marks are represented by (X.sub.1, Y.sub.1), (X.sub.2, Y.sub.2), (X.sub.3, Y.sub.3), and (X.sub.4, Y.sub.4), respectively. On the other hand, the detection coordinates of the matching mark positions in the block which is actually detected are represented by (x.sub.1, y.sub.1), (x.sub.2, y.sub.2), (x.sub.3, y.sub.3), and (x.sub.4, y.sub.4), respectively.
By applying the correcting equations (the equations 1) to the design mark coordinates (X.sub.i, Y.sub.i) and the actually detected mark coordinates (x.sub.i, y.sub.i), the following equations are obtained. ##EQU2##
From these eight equations, eight unknowns A to D' are calculated by a method of least squares. The foregoing procedure is executed every matching block, thereby realizing the high accurate pattern matching among the layers.
In general, as mentioned above, the matching marks at four corners in the matching block are detected to obtain the correction coefficients and the matching drawing is executed. However, when this method is actually applied, there is a case where some of the matching marks at four corners are not detected because of the reasons such as breakage of matching marks and the like. As will be understood from the equations (2), if a detection error occurs even in one of the four matching marks, the correction coefficients A to D' as eight unknowns cannot be calculated. Hitherto, when such a mark error occurs, the relevant block is not drawn and the process advances to the shift block, or it is drawn by using the correction coefficients of the preceding block.